Frustrated magnetic order in hybrid Kitaev spin-orbital models

TL;DR

This paper explores how combining different exactly solvable Kitaev-related models on various lattices leads to new magnetic and topological phases, including magnetic order and Majorana band evolution.

Contribution

It investigates the effects of hybridizing Kitaev and Yao-Lee models on different lattices, revealing emergent phases and conditions for exact solvability.

Findings

Strong-Kitaev regime induces magnetic order with topological orbital sectors.

Hybrid models show evolution of Majorana bands and Lifshitz transitions.

Equal and opposite couplings restore exact solvability with a single Majorana flavor.

Abstract

Spin-orbital generalization of Kitaev model provides a robust extension to the original Kitaev model. However, real materials often exhibit competing interactions that break exact solvability which can give rise to new phases. Motivated by recent microscopic proposals of coexisting Yao-Lee and Kitaev couplings, we investigate the fate of the ground state when two independent exactly solvable spin liquid Hamiltonians each originally formulated on different lattice geometries are combined on a common lattice environment. We first focus on the hybrid Kitaev's honeycomb and square-lattice model. Using self-consistent mean-field analysis and perturbative calculation, we show that the strong-Kitaev regime yields magnetic order in the spin sector, while the orbital sector retains its topological order. We further analyze the hybridization of the Yao-Lee and square-lattice models and find that the model exhibits a rich evolution of Majorana Dirac bands and Lifshitz transitions. Remarkably, when the Yao-Lee and square-lattice couplings are equal and opposite, the model restores its exact solvability with a single itinerant Majorana flavor. These results demonstrate that hybrid spin liquid platforms may host various emergent phases beyond conventional exactly solvable limits.